Out of context, getting to live forever and never having to worry about death and necessity ever again seems like a good deal. But in fiction, especially in anime, it's common to add some horrible, ironic catch to it to make it less than ideal.
Sometimes, an immortal character can still get hurt and feel pain. In fact, it makes things all the worse because they can survive things that would normally kill a person. Often, this gets to a point where a character can technically even die but come back to life soon after. Another popular twist is to have an immortal character still endure the effects of aging or be stuck as a child. Added to this, an immortal character might actually be very powerful but has been weakened by some mental or spiritual trauma.
10 Anthy Endures The Hatred Of Humanity As She's Stuck As The Rose Bride (Revolutionary Girl Utena)
In Anthy's backstory, she is the witch who sealed away her brother, the prince, and has to endure the hatred of humanity, which comes in the form of millions of invisible swords. She is also the immortal Rose Bride, being the holder of the Sword of Dios, and is at the mercy of her now villainous brother. Her true self is kept in a coffin.
That said, she's actually quite powerful, but the trauma she's endured keeps her from rebelling for hundreds of years, at least outside of a passive-aggressive manner.
9 Falling In Love Ultimately Trapped Majo Tourbillon In A Death-Like Sleep (Ojamajo Doremi)
Majo Tourbillon, who was once the kindhearted Witch Queen, normally would have had the more positive form of immortality, as she doesn't seem to physically age. However, she fell in love with a human, and the trauma of outliving both him and her human son trapped her in a death-like sleep.
Even in this stasis, however, her magic proves to be quite powerful, as she's capable of casting powerful curses on the characters. She's especially determined to keep contact between the witches and humans as forbidden as possible to prevent other witches from similar hardships.
8 Dallas Genoard Is An Incomplete Immortal (Baccano)
In a series filled with immortal characters, Dallas has an incomplete version of immortality: he will recover from any wound, but still ages. With him getting kicked around by other characters, Dallas laments how weak this makes him, once considering himself the weakest being on earth, especially since truly immortal characters can kill him but not vice-versa.
Notably, at one point, he gets shoved in a barrel with cement and dumped in the Hudson River. Thanks to his ability, this puts him in a constant state of drowning until he gets rescued.
7 Joseph/Cartaphilus Is Basically A Living Corpse (The Ancient Magus' Bride)
Joseph/Cartaphilus is a mysterious wizard who cannot die, but his body has become like a living corpse, forcing him to constantly renew or replace his body parts, as he especially cannot grow new ones. It appears that he cannot even move without replacements.
Adding to the horror, being hit with special bullets can prevent him from regenerating a missing body part. It ultimately turns out his condition is partially from being two people fused together. That said, despite the physical horror, he's actually quite skilled when it comes to magic. He also has an affinity with insects, but it's unclear if that's magic or they're attracted to his rotting flesh.
6 Sakura Has A Tricky Form Of Immortality (Bludgeoning Angel Dokuro-Chan)
Sakura has a very complicated form of immortality. The titular angel, Dokuro, is tasked with killing him to prevent a horrible future he's destined to create, but she's also fallen in love with him, and so always uses her powers to keep him alive, even after violently bludgeoning him.
The light novels and manga also add a twist: Dokuro doesn't merely bring him back to life from these attacks. Thanks to her powers, Dokuro never actually kills him and he's alive and conscious even as he's being turned into a bloody mess.
5 Cyborg 001 Appears To Be Stuck As A Baby (Cyborg 009)
The trauma of becoming a cyborg is showcased throughout the series. One of the characters who probably got the cruelest deal is Cyborg 001, who, due to being experimented on by his father, is stuck as a baby.
To make up for this lack of physical ability, he has tremendous psychic powers and mental prowess which have sometimes saved the day. Unfortunately, using his powers also put immense trauma on his body, causing him to sleep for days at a time, meaning his powers can only be used as a last resort.
4 Sailor Moon: Chibiusa Is The Weakest Sailor Scout Despite Being 900
Chibiusa, being a time-traveler from Crystal Tokyo, is effectively immortal, considering she's at least around 900 years old in the manga. Exactly how aging works for her is unclear, but it seems she won't reach maturity at least until she awakens into her powers.
Given how long it took for her to become a Sailor Scout, Sailor Chibi Moon, she appears to be the weakest of the Sailor Senshi, with her powers either outright failing to work at worst or her functioning as support for the other Scouts at best. That said, she'll presumably grow out of this, so she'll eventually have the more positive form of immortality.
3 Hidan Ended Up As Just A Head In A Hole & He'll Probably Rot, Too (Naruto)
Hidan originally had the power of immortality, being able to reattach his limbs, including his own head. The only catch seems to be that he has to keep killing people or he'll become mortal again. However, Shikamaru found a workaround with this: he just has to bury his head in a pit, with his clan ensuring that it won't be found.
To rub salt in the wound, supplementary material implied he'll eventually starve to death anyway, meaning he even loses his immortality. He might even start to rot before this happens.
2 Elder Toguro Is A Bit Of A Bait-And-Switch (Yu Yu Hakusho)
Elder Toguro initially appears to be horribly weakened in spite of his immortality: he rides around on his brother and the manga also portrays him as unnaturally small. However, this is just an act and he's actually quite powerful, especially when it comes to shapeshifting.
However, his immortality is ultimately used against him: Kurama attacks him with a parasitic plant that will drain his life energy while trapping him in a vision. Since he's immortal, he'll be trapped in this state forever.
1 Garlic Jr. Ends Up Withered In The Dead Zone (Dragon Ball)
Garlic Jr. was able to obtain immortality, but his luck would soon run out. While attempting to trap his enemies into the Dead Zone, Gohan managed to trap him in his own vortex, trapped in eternal darkness, leaving him a withered husk.
While he eventually manages to escape in the anime, he ultimately ends up trapped in the Dead Zone all over again without any chance of escaping.